N6NumberFoundation & Higher

Percentages

“Per cent” means “out of 100”. Percentages are everywhere — discounts, interest, test scores — so being quick with them is one of the most useful GCSE skills.

40 min Video by Maths Genie AQA GCSE Maths

Finding a Percentage of an AmountWatch the walkthrough, then read the notes below.

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What you'll learn

Find a percentage of an amount
Increase and decrease by a percentage
Use multipliers
Find the original amount (reverse percentages)

Percentage of an amount

To find a percentage, turn it into a decimal and multiply. $25%$ of $80$ is $0.25 \times 80 = 20$ . The decimal you multiply by is called the $multiplier$ .

Increase, decrease and multipliers

To increase by $20%$ , multiply by $1.2$ . To decrease by $20%$ , multiply by $0.8$ . Multipliers make multi-step problems (like compound interest) much faster.

new = original \times multiplier

e.g. +15% → ×1.15, −15% → ×0.85.

1Decrease by 30% → multiply by

0.7

40 \times 0.7 = 28

Answer£28

Tip — For reverse percentages, divide by the multiplier instead of multiplying.

Remember these

+ p % \to \times (1 + \frac{p}{100})

Increase multiplier.

- p % \to \times (1 - \frac{p}{100})

Decrease multiplier.

Watch out for these

Finding 30% off then forgetting to subtract it from the original.

Multiply by 0.7 directly to get the new amount in one step.

Reversing a percentage by adding it back on.

Divide by the multiplier to undo a percentage change.

Key takeaways

Percent means out of 100 — convert to a decimal and multiply.
Increase: ×(1 + p/100); decrease: ×(1 − p/100).
Reverse percentages divide by the multiplier.

Test yourself

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